Discrete model reference adaptive control of continuous-time linear multi-input multi-output systems via multirate sampled-data controllers

The use of multirate sampled-data controllers for linear multivariable time-invariant systems with unknown parameters is investigated. Such controllers contain periodically time-varying elements and a multirate sampling mechanism with different sampling periods at each system input. Their application to unknown continuous-time linear multi-input, multi-output systems results in a sampled closedloop system for which an arbitrary discrete-time transfer function matrix can be assigned, as is shown in the present paper. The contribution of the present paper is twofold: the use of multirate sampled-data controllers in the area of model reference adaptive control; and the application, for the first time, of periodically varying controllers for model reference adaptive control of multi-input, multi-output systems.The work described in this paper has been partialy funded by the General Secretariat for Research and Technology of the Greek Ministry of Industry, Research, and Technology and by the Heracles General Cement Company of Greece.     

Adaptive decoupling of linear systems using multirate generalized sampled-data hold functions

An indirect adaptive controller synthesis algorithm is derivedfor the decoupling of linear multivariable time-invariant systemswith unknown parameters using multi-rate generalized sampled-datahold functions. Such controllers contain a multirate samplingmechanism with different sampling period at each system inputand two periodically varying modulating matrix functions. Thealgorithm proposed in the paper estimates the modulating functionson line, and ensures persistent excitation of the continuous-timeplant without making any assumption on the reference signals.The only prior knowledge needed is the minimality of the continuousand sampled system, known order, and a set of structural indices,namely the locally minimum controllability indices of the continuous-timepalnt.     

Stability analysis of impulsive control systems

This paper studies impulsive control systems. Several stability criteria are established by employing the method of Lyapunov functions. These criteria may be used for impulsive feedback control design. As an application, impulsive control of the Lorenz chaotic system is discussed. Numerical experiments are carried out for the control of the Lorenz system. It is shown that small and frequent impulses need to be used in order to stabilize the Lorenz system.     

Discrete observer in the design of sampled-data control systems

This paper considers the problem of designing a feedback controller for sampled-data systems by using a discrete observer. Longitudinal control of an automated transit vehicle is used as an example to discuss the application of the discrete-observer design.     

Stability analysis and optimal control of stochastic singular systems

In this paper, problems of stability and optimal control for a class of stochastic singular systems are studied. Firstly, under some appropriate assumptions, some new results about mean-square admissibility are developed and the corresponding LMI sufficient condition is given. Secondly, finite-time horizon and infinite-time horizon linear quadratic (LQ) control problems for the stochastic singular system are investigated, in which the coefficients are allowed to be random in control input and quadratic criterion. Some results involving new stochastic generalized Riccati equation are discussed as well. Finally, the proposed LQ control model for stochastic singular systems provides an appropriate and effective framework to study the portfolio selection problem in light of the recent development on general stochastic LQ problems.     

Stability analysis of sampled-data fuzzy controller for nonlinear systems based on switching T–S fuzzy model

This paper investigates the system stability of a sampled-data fuzzy-model-based control system, formed by a nonlinear plant and a sampled-data fuzzy controller connected in a closed loop. The sampled-data fuzzy controller has an advantage that it can be implemented using a microcontroller or a digital computer to lower the implementation cost and time. However, discontinuity introduced by the sampling activity complicates the system dynamics and makes the stability analysis difficult compared with the pure continuous-time fuzzy control systems. Moreover, the favourable property of the continuous-time fuzzy control systems which is able to relax the stability analysis result vanishes in the sampled-data fuzzy control systems. A Lyapunov-based approach is employed to derive the LMI-based stability conditions to guarantee the system stability. To facilitate the stability analysis, a switching fuzzy model consisting of some local fuzzy models is employed to represent the nonlinear plant to be controlled. The comparatively less strong nonlinearity of each local fuzzy model eases the satisfaction of the stability conditions. Furthermore, membership functions of both fuzzy model and sampled-data fuzzy controller are considered to alleviate the conservativeness of the stability analysis result. A simulation example is given to illustrate the merits of the proposed approach.     

Stochastic stability and robust control for sampled-data systems with Markovian jump parameters

In this paper, the problems of stochastic stability and robust control for a class of uncertain sampled-data systems are studied. The systems consist of random jumping parameters described by finite-state semi-Markov process. Sufficient conditions for stochastic stability or exponential mean square stability of the systems are presented. The conditions for the existence of a sampled-data feedback control and a multirate sampled-data optimal control for the continuous-time uncertain Markovian jump systems are also obtained. The design procedure for robust multirate sampled-data control is formulated as linear matrix inequalities (LMIs), which can be solved efficiently by available software toolboxes. Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed techniques.     

Stability of neutral-type nonlinear control systems

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 6, pp. 848–853, June, 1989.     

Stability of discrete nonlinear control systems

The paper considers multiple-input multiple-output discretesystems with nonlinearities confined to sectors and with linearparts having parameter uncertainties. A recently dervied mathematicaltool, the determination of zero-sets location, is used to obtainthe complete feasible set of sectors of the nonlinearities whichmaintain robust absolute stability, according to Tsypkin's criterion.Moreover, for flexibility of design, this set is influencedand controlled by an internal feedback loop. This feedback loopmay also serve as a stabilizer of the linear part, if necessary .A numerical example is provided.     

Stability analysis of queueing systems

This paper contains a survey of some results on the stability of queueing systems obtained by the authors by means of the method of trial functions (developed from Lyapunov's direct method). In addition, the paper contains a series of new results on the stability of regenerative processes. All the qualitative statements are accompanied by the construction of quantitative estimates.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 87, pp. 41–61, 1979.     

Model reduction techniques for sampled-data systems

An approximately balanced realization of linear finite-dimensional sampled-data systems is proposed. The theoretical support of the approximately balancing algorithm is represented by a result on the asymptotic expansions with respect to the sampling step of the sampled controllability and observability graminas. Reduced order models obtained as singular perturbational approximations of approximately balanced realizations of sampled-data systems are shown to be acceptable solutions to the sampled-data system model reduction problem in the sense that, enjoying some asymptotic properties, they come close to the exact solutions as the sampling step decreases. An example illustrates the results.     

Stability analysis and control synthesis for a class of switched neutral systems

In this paper, the problems of asymptotical stability and stabilization of a class of switched neutral control systems are investigated. A delay-dependent stability criterion is formulated in term of linear matrix inequalities (LMIs) by using quadratic Lyapunov functions and inequality analysis technique. The corresponding switching rule is obtained through dividing the state space properly. Also, the synthesis of stabilizing state-feedback controllers are done such that the close-loop system is asymptotically stable. Two numerical examples are given to show the proposed method.     

Low-order self-tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems

Based on the modified state-space self-tuning control (STC) via the observer/Kalman filter identification (OKID) method, an effective low-order tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems is proposed in this paper. The OKID method is a time-domain technique that identifies a discrete input–output map by using known input–output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm (ERA). Then, the above identified model in a general coordinate form is transformed to an observer form to provide a computationally effective initialization for a low-order on-line “auto-regressive moving average process with exogenous (ARMAX) model”-based identification. Furthermore, the proposed approach uses a modified Kalman filter estimate algorithm and the current-output-based observer to repair the drawback of the system multiple failures. Thus, the fault-tolerant control (FTC) performance can be significantly improved. As a result, a low-order state-space self-tuning control (STC) is constructed. Finally, the method is applied for a three-tank system with various faults to demonstrate the effectiveness of the proposed methodology.     

Model simplification and digital design of multivariable sampled-data control systems via a dominant-data matching method

A dominant-data matching method is developed for model simplification and design of digital multivariable sampled-data control systems. A mixed method combining dominant-data matching and the dominant-pole technique is also derived for determining a stable reduced-degree multivariable digital controller. A real semiactive terminal homing missile system is used as an illustrative example.     

Stability of impulsive control systems with variable times

In this paper, cone-valued Lyapunov functions are employed to study the impulsive control system with variable times. The stability criteria on the non-zero solution of the impulsive control system are given by the cone-valued Lyapunov functions and the results of the controllability on the control system are also obtained.     

Stability of backward Euler multirate methods and convergence of waveform relaxation

For a large class of traditional backward Euler multirate methods we show that stability is preserved when the methods are applied to certain stable (but not necessarily monotonic) non-linear systems. Methods which utilize waveform relaxation sweeps are shown to be stable and converge for certain monotonic systems.